The present invention pertains to position location systems and more particularly to a method for eliminating false positions detected in a hyperbolic positioning system.
Most positioning systems utilizing radio frequency or sound to position objects are hyperbolic, which means that the timing relationships between multiple signals to or from multiple sites with fixed timing relationships form sets of intersecting hyperbolas. This is true in cases where multiple transmissions from reference points are received at an unknown location, such as the GPS, LORAN, and the MOTOROLA CATIES (Combined Arms and Training Integrated Evaluation System) systems, or when a single transmission from an unknown location is received at multiple reference points, such as the RDMS (Range Data Measurement System) at the US Army National Training Center.
This hyperbolic nature can be demonstrated using a typical multi-lateration scheme in which signals are transmitted omni-directionally from several stationary transmitters with a specific timing relationship. As signals from each transmitter propagate at the speed of light away from the transmitters, receivers measuring the timing relationship between two signals would, measure identical intervals at a locus of points. The formula for this set of points is D1-D2=K1, where D1 is the distance from transmitter #1, D2 is the distance from transmitter #2, and the constant K1 is the difference in timing between the two signals. This equation is, in two dimensions, a hyperbola. These two signals are insufficient to determine position since it cannot be established where on the hyperbola the receiver resides. Another data point is required from another transmitter. Using one of the three received signals (#1) as a time reference results in two intersecting hyperbolas (D1-D2=K1, and D1-D3=K2). The receiver can then use the measured time intervals to determine the location where the two hyperbolas meet. The intersection of two hyperbolas is not directly solvable so an iterative method such as least squares is used to drive the solution from an initial estimate towards the location that comes closest to meeting the measured timing data. Under most circumstances, the location converges towards the true location of the receiver.
Since hyperbolas are not straight lines, there is a high probability that they intersect at more than one location. By definition, both intersections share the exact same timing relationships and a receiver at either location cannot differentiate between them purely by measuring the timing intervals. Most of the time the system will resolve the correct location because the second intersection is sufficiently far away or the initial estimate is close to the true location. In general, large baselines and/or good geometries as defined by low Dilution Of Precision (DOP) values and filtering of previous position data reduce the probability of resolving to a false location, they do not prevent false locations from being detected.
Several methods used in multi-lateration systems that increase the accuracy of the positioning and provide some protection against false positioning are large baselines, using more than three transmitters, filtering data over time, and utilizing quantitative geometric selection methods. These are discussed below with respect to false positioning.
1. Large geometries, such as GPS and LORAN, are susceptible to false positions, but since the distance between the system elements is so large, the curvature of the hyperbolas is small and the second intersection is very far away. PA1 2. Using more than three transmitters provides more timing data which usually results in more accurate positions. It also provides some redundancy so that three or more signals are received, even if one or more are blocked. This method reduces the chances of false positions somewhat because if all the signals are received, more hyperbolas are created. Four transmitters causes three hyperbolas and it is far less likely that three separate hyperbolas will intersect at the same two locations. Five or more transmitters reduce the chances even more. PA1 3. Another method designed to increase positioning accuracy is to pick an optimum geometry to minimize errors. Common methods such as Horizontal Dilution of Precision (HDOP) mathematically select a set of transmitters with the most diverse angular spacing around the area in which positioning is desired. This also has the effect of selecting hyperbolas that intersect at the largest angles, thus reducing the chances that the hyperbolas will intersect nearby. The major weakness of algorithms such as HDOP is that they are valid at the intersection of the hyperbolas only and do not give any indication of how fast the geometry degrades in a specific direction to the point where a false positioning may occur. It also assumes all signals are received. PA1 4. Filtering the data over time allows previous positions to be used to generate an initial position estimate instead of the intersection of the hyperbolas. If the previous position is accurate, it significantly increases the chances that the algorithm converges to the correct location. It also allows large jumps caused by an erroneous position to be discarded.
While additional transmitters, geometrical selection, and filtering work well in theory, they do not always perform well in actual situations because signal blockages from hills, buildings, foliage, and vehicles can reduce the number of signals received. Also, large geometries, such as satellites, are not always practical. What is needed in these situations is a method to predict situations where insufficient timing data can result in false positions in real time or that can use the data set to select the optimum data to generate a unique solution.